The first time I heard about that, was back in 2000. Ilidio Lopes and Joe Silk, both at the U. of Oxford, told me about the interesting effects that WIMPs could have on the structure of the Sun. Ilidio and I included the effect of capture and annihilation of Dark Matter particles in a solar evolutionary code, but it turned out that the most interesting region of the DM parameter space did not lead to observable effects (see the paper here).
I kept thinking about DM and stars for a while, and while at FNAL I discussed a lot about this issue with John Beacom and Lam Hui. Batavia maybe is not as charming as Lisbon, but Chicago is not far, and there you might enjoy this.
Finally, Malcolm Fairbairn (who was working independently on the same ideas) and I published a paper on the effect of DM on Compact Objects such as White Dwarfs and Neutron Stars.
Recently, then, prompted by an interesting paper of I. Moskalenko and L. Wai, many groups have started working on the effect of DM on different types of stars. In particular D. Spolyar, K. Freese and P. Gondolo have shown that DM annihilations could have a dramatic impact on the evolution of Population III stars (the image above, taken from this website, shows a simulation of the formation of a Pop III star in a standard astrophysical scenario).
With the help of Georges Meynet and Sylvia Ekstrom of the Geneva Observatory, Marco Taoso (a PhD student at IAP) and I have performed a detailed analysis of the capture and annihilation of DM in Pop III stars, and have found that these stars could remain “frozen” for timescales longer than the age of the Universe. Cool, eh?
More about our results in this New Scientist article.